Learning and the Value of Trade Relationships Ryan Monarch

Tim Schmidt-Eisenlohr

Federal Reserve Board

Monarch / Schmidt-Eisenlohr (FRB)

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Any opinions and conclusions expressed herein are those of the author and do not necessarily represent the views of the U.S. Census Bureau, the Federal Reserve Board, or anyone affiliated with the Federal Reserve System. All results have been reviewed to ensure that no confidential information is disclosed.

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Every commercial shipment is based on a relationship between a firm and its supplier.

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Every commercial shipment is based on a relationship between a firm and its supplier. But relationships are not equal: some are very short, while others grow and prosper over decades. We explore long-term success in relationships- using panel data on importers and exporters. Why do we care about long-term relationships?

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Every commercial shipment is based on a relationship between a firm and its supplier. But relationships are not equal: some are very short, while others grow and prosper over decades. We explore long-term success in relationships- using panel data on importers and exporters. Why do we care about long-term relationships? I

Most trade (that we can track) is in long-term relationships. Table: U.S. Arm’s-Length Imports, 2011

Share of Value

Monarch / Schmidt-Eisenlohr (FRB)

New 21.8

1-2 Years 30.6

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3+ Years 47.6

3/ 39

Every commercial shipment is based on a relationship between a firm and its supplier. But relationships are not equal: some are very short, while others grow and prosper over decades. We explore long-term success in relationships- using panel data on importers and exporters. Why do we care about long-term relationships? I

Most trade (that we can track) is in long-term relationships. Table: U.S. Arm’s-Length Imports, 2011

Share of Value I

New 21.8

1-2 Years 30.6

3+ Years 47.6

Within a relationship, the amount traded increases with age.

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Long-Term Relationships are Also More Resilient Table: Total Number of Relationships, 2007-2010 Year Relationship Counts New Relationship Counts Continuing-Relationship Counts

Monarch / Schmidt-Eisenlohr (FRB)

2007 1 1 1

2008 0.97 0.93 1.03

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2009 0.90 0.85 0.97

2010 0.98 0.96 0.99

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Long-Term Relationships are Also More Resilient Table: Total Number of Relationships, 2007-2010 Year Relationship Counts New Relationship Counts Continuing-Relationship Counts

2007 1 1 1

2008 0.97 0.93 1.03

2009 0.90 0.85 0.97

2010 0.98 0.96 0.99

Long-Term Relationships Matter!

Monarch / Schmidt-Eisenlohr (FRB)

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In this paper we: Generate a new set of stylized facts about buyer-supplier relationships, using the universe of U.S. import data. Use the Araujo et. al. (2012) learning framework to build in dynamic adjustments within a relationship. Calibrate key parameters of the model to assess the quantitative importance of learning. Run counterfactual experiments that underscore the importance of sustained relationships to aggregate dynamics.

Ultimate Goal: Calculate the value to importers of being in a relationship, and how much this contributes to international trade and its dynamics.

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Preview of Results: Long-term relationships are, on average, 7.2 times more valuable than new relationships. I

I

An importer would pay that much for the partner-specific knowledge embodied in a long-term relationship. Varies widely by individual country.

One successful year of experience with a Chinese supplier is more valuable than one year with a German supplier. I

Since most relationships with Chinese suppliers fail right away, the learning boost from a successful relationship is high.

If long-term relationships were completely reset, the total trade lost over 10 years would be 1.5 times the annual level of U.S. imports.

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Literature Networks in international trade: Rauch (2001), Rauch and Watson (2004), Chaney (2014) Experience and learning in trade: Egan and Mody (1992), Rauch and Watson (2003), Besedes and Prusa (2006), Besedes (2008), Albornoz et al. (2012), Araujo et al. (2012), Blum et al. (2013), Impulitti et al. (2013), Timoshenko (2014), Machiavello and Morjaria (forthcoming) “Two-sided” trade data: Eaton et al. (2014), Kamal and Krizan (2012), Kamal and Sundaram (2013), Carballo et al. (2013), Monarch (2014), Bernard et al. (2014) Trade dynamics: Ghironi and Melitz (2005), Alessandria and Choi (2007), Ruhl (2008), Ruhl and Willis (2008), Atkeson and Burstein (2010), Eaton et al. (2011), Alessandria et al. (2015)

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Data

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U.S. import data is from the Linked-Longitudinal Foreign Trade Transaction Database (LFTTD). Each transaction contains (a) (b) (c) (d)

Value and quantity (and thus “unit value”) HS 10 industry code. Unique exporter identifier (known as Manuf. ID). Exporter location (city) information.

Example: QUAN KAO COMPANY 1234 BEIJING LANE BEIJING, CHINA 100044

Monarch / Schmidt-Eisenlohr (FRB)

CNQUAKAO1234BEI

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Definition: An importer is a U.S. importing firm. Definition: An exporter is a foreign exporting firm exporting to the U.S. Definition: A relationship is an importer-exporter combination.

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Empirical Patterns: Aggregate Relationship Structure of Trade

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Table: Relationship Structure of U.S. Imports, 2011

Share of Relationships Share of Trade

New 57.6 21.8

1-2 Years 26.9 30.6

3 or More Years 15.6 47.6

Most trade relationships are new Trade is most concentrated in long-term relationships

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Table: Relationship Structure of U.S. Imports, 2011

China Spain Mexico Canada France Japan Germany Chile Thailand Taiwan

% Counts, 3+ Year Relationships 0.11 0.13 0.17 0.17 0.17 0.20 0.20 0.21 0.22 0.24

Spain China Venezuela Korea Canada Germany Thailand Japan Mexico Taiwan

% Trade, 3+ Year Relationships 0.33 0.33 0.45 0.45 0.47 0.49 0.56 0.62 0.65 0.67

Varies widely across countries. Monarch / Schmidt-Eisenlohr (FRB)

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Figure: Evolution of Trade Within a Relationship

0.7 0.6

Value traded

0.5 0.4 0.3 0.2 0.1

5-year 7-year 10-year 13-year

0.0 0.1 0.2

0

1

2

3

4

5

6

7

Age

8

9 10 11 12 13

Trade increases as a relationship ages. Monarch / Schmidt-Eisenlohr (FRB)

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Figure: Relationship Survival Probabilities 0.9

Survival probability

0.8 0.7 0.6 0.5 0.4 0.3

0

1

2

3

4

5

Age

6

7

8

9

10

Survival probability increases as a relationship ages.

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Table: Determinants of Importer-Exporter Relationship Age, 2011

RuleOfLawc PC − GDP c ImporterSize ImporterAge ImporterNoProducts ExporterSize ExporterRelCount N Fixed Effects Monarch / Schmidt-Eisenlohr (FRB)

(1) 0.122

(2) 0.124

(3) 0.119

(4) 0.126

(0.012)**

(0.013)**

(0.016)**

(0.012)**

0.073

-0.006

0.031

(0.019)**

(0.014)

(0.011)**

-0.027

-0.027

-0.027

-0.026

(0.026)

(0.026)

(0.026)

(0.025)

0.044

0.044

0.044

0.045

(0.005)**

(0.004)**

(0.004)**

(0.004)**

0.296

0.297

0.297

0.298

(0.053)**

(0.053)**

(0.053)**

(0.052)**

0.232

0.233

0.233

0.234

(0.013)**

(0.013)**

(0.013)**

(0.013)**

-0.376

-0.378

-0.379

-0.383

(0.016)**

(0.016)**

(0.016)**

(0.016)**

1,075,100 HS2

1,075,100 HS2

1,075,100 HS2

1,075,100 HS2

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What happened in the Trade Collapse? Table: Relationship Margins Year Relationship Counts New Relationship Counts Continuing-Relationship Counts Ending-Relationship Counts

Monarch / Schmidt-Eisenlohr (FRB)

2007 1 1 1 1

2008 0.97 0.93 1.03 1.02

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2009 0.90 0.85 0.97 1.02

2010 0.98 0.96 0.99 0.88

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What happened in the Trade Collapse? Table: Relationship Margins Year Relationship Counts New Relationship Counts Continuing-Relationship Counts Ending-Relationship Counts

2007 1 1 1 1

2008 0.97 0.93 1.03 1.02

2009 0.90 0.85 0.97 1.02

2010 0.98 0.96 0.99 0.88

Table: Survival Probabilities During the Trade Collapse Relationship Age Crisis CrisisXRule of Law Age Fixed Effects N R2 Monarch / Schmidt-Eisenlohr (FRB)

0-2 -0.051

3-5 -0.056

(0.008)**

(0.014)**

(0.015)

0.019

0.043

-0.012

(0.008)*

(0.014)**

(0.012)

Yes 654 0.54

Yes 963 0.08

Yes 1605 0.03

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6+ -0.007

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Model

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Basic Setup: Technology

Consider a relationship between one importer and one exporter The exporter: Produces intermediate inputs Decides on whether to exert effort in production: I

Effort gives rise to production costs c1 , which are repaid by the buyer

The importer: Hires other inputs at cost c2 in advance Assembles intermediate inputs into final good Relationships die exogenously at rate δ.

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Basic Setup: Bayesian Updating Only θb of suppliers are reliable. t=0

I I I

t=1

I I I

Importer and exporter agree on a trade: (price and quantity) Importer pays the exporter fraction α in advance Exporter receives money and decides whether to exert effort ⇒ reliable supplier always exerts effort ⇒ myopic supplier only exert efforts when forced (probability λ) Importer receives goods and realizes profits Importer pays remaining amount (1 − α) if received good quality input: update beliefs (Bayes’ Rule) and trade again next period

The posterior probability that a supplier is patient after buying from them for k periods is: θk =

Monarch / Schmidt-Eisenlohr (FRB)

θb 

 θb + 1 − θb λk

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(1)

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Delivery probability Call θek = θk + (1 − θk ) λ the delivery probability. I I

I

θk is the probability that the supplier is patient. (1 − θk ) λ is the probability that the supplier is not patient but the importer receives the inputs anyways. θek increases in k: Figure: Delivery Probabilities 1.0

˜θ

0.8 0.6 0.4 0.2

low λ high λ 1

Monarch / Schmidt-Eisenlohr (FRB)

2

3

4

5

6

Age

7

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8

9

10

11 21/ 39

Expected profits from a supplier used for k periods: E [πk ] = θek (R (q) − (1 − α)c1 q) − (αc1 + c2 ) q

(2)

FOC implies: R 0 (q) = (1 − α)c1 +

Monarch / Schmidt-Eisenlohr (FRB)

αc1 + c2 θek

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(3)

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CES

Assume now that we have the following CES aggregator: Z

σ−1 σ



σ σ−1

dω

(4)

qt,k = pk−σ Ptσ Qt ,

(5)

Q=

q(ω) Ω

This delivers the standard demand:

with P =

1−σ Ω p(ω)

R

Monarch / Schmidt-Eisenlohr (FRB)




1 1−σ

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The optimal price is then:   αc1 + c2 σ (1 − α)c1 + pk = σ−1 θek

(6)

Revenues (in case of successful production) are:  Rk =

σ σ−1

Monarch / Schmidt-Eisenlohr (FRB)

1−σ 

 αc1 + c2 (1 − α)c1 + PσQ e θk

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Model moments Survival from k to k + 1 (with exogenous death probability δ): survk = (1 − δ)θek How many relationships of age k are alive at any time:     k k b b alivek = alivek−1 ∗ survk−1 = (1 − δ) λ 1 − θ + θ Age-shares: agesharek = alivek /

K X

alives

s=0

Trade-shares: tradesharek = (Rk alivek ) /

K X

(Rs alives )

s=0

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The Inherent Value of a Relationship How much would an importer pay to have the accumulated knowledge about a supplier inherent in a long-term relationship? Compare profit streams for new and long-term relationships: Perfect Knowledge: o

E[Π ] =

∞ X

(1 − δ)k E [πk ]

(8)

k=0

=

A δσ



σ σ−1

1−σ

[c1 + c2 ]1−σ .

New Relationship: E[Πn ] =

∞ X

alivek E [πk ] =

(9)

k=0

A σ



1−σ X 1−σ ∞    σ ˆ + θˆ θ˜k (1 − α)c1 + αc1 + c2 (1 − δ)k λk (1 − θ) . ˜k σ−1 θ k=0

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E[Πn ] is always less than E[Πo ]: The relationship survival probability is higher with a patient supplier. The importer orders more and generates larger expected revenues and profits. The inherent value of a relationship is: [c1 + c2 ]1−σ E[Πo ] = × E[Πn ] δ 1−σ !−1 ∞    X αc + c 1 2 k k ˆ + θˆ θ˜k (1 − α)c1 + (1 − δ) λ (1 − θ) . ˜k θ k=0 IV =

ˆ Decreasing in θ.

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Calibration

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Solve the following problem: N X \ k )2 , (agesharek − ageshare

Error 1 =

Error 2 =

k=1 N X

\ k )2 (tradesharek − tradeshare

k=1

↓ arg min

ˆ δ,θ,λ

βError 1 + (1 − β) Error 2

where ageshare and tradeshare are the values predicted by the model \ and tradeshare \ are taken from the data. and ageshare Run this algorithm for the top 20 trading partners of the U.S.

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Can generate model predictions for Age and Trade Shares.

2

3

0

1

2

3

Age

4

5

6

7

4

5

6

7

Value Share

1

Age

Mexico

0

1

2

3

0

1

2

3

Age

4

5

6

7

4

5

6

7

Value Share

Value Share

Canada

0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.25 0.20 0.15 0.10 0.05 0.00

0

1

2

3

0

1

2

3

Age

Age

4

5

6

7

4

5

6

7

4

5

6

7

4

5

6

7

Japan

Count Share

Value Share

0

Count Share

0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.25 0.20 0.15 0.10 0.05 0.00

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.25 0.20 0.15 0.10 0.05 0.00

Count Share

China

Count Share

0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.30 0.25 0.20 0.15 0.10 0.05 0.00

Age

Monarch / Schmidt-Eisenlohr (FRB)

0

1

2

3

0

1

2

3

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Age

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.2

.25

Lambda .3 .35

.4

.45

Our country-specific λ estimates line up well with measures of institutional quality (R 2 =0.41).

-2 Monarch / Schmidt-Eisenlohr (FRB)

-1

0 Rule of Law Learning in International Trade

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Inherent Values Table: Parameters and the Value of Relationships

Country Canada Chile China Germany Spain France Japan Korea Mexico Netherlands Philippines Thailand Taiwan

(1)

(2)

(3)

λ 0.17 0.16 0.06 0.24 0.32 0.32 0.23 0.22 0.20 0.37 0.02 0.15 0.20

θˆ 0.18 0.33 0.36 0.23 0.09 0.10 0.16 0.18 0.13 0.09 0.44 0.24 0.25

δ 0.23 0.27 0.33 0.21 0.21 0.17 0.14 0.23 0.11 0.23 0.32 0.17 0.14

(4) Value of a New Relationship 0.33 0.54 0.46 0.49 0.20 0.31 0.54 0.35 0.58 0.21 0.61 0.65 0.88

(5) Value of an Old Relationship 2.56 2.16 1.79 2.76 2.82 3.54 4.09 2.61 5.36 2.60 1.84 3.45 4.22

(6) Inherent Value of a Relationship 7.73 4.00 3.88 5.69 13.83 11.56 7.61 7.54 9.26 12.44 3.04 5.3 4.78

Long-term relationship profits are 7.2 times higher on average. Monarch / Schmidt-Eisenlohr (FRB)

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How Do Expected Profits Change with Age 3.0

Expected profits

2.5 2.0 1.5 1.0

China Germany Spain

0.5 0.0

0

1

2

3

Age

4

5

6

One year of history with a Chinese supplier boosts profits significantly. Long term profits are higher with German suppliers. Monarch / Schmidt-Eisenlohr (FRB)

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Counterfactuals

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Counterfactuals: Partial equilibrium (exogenous entry), but allowing price level to adjust Change entry path and / or initial distribution Move back to steady-state entry levels Study time path back to steady state trade levels

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Counterfactuals: Partial equilibrium (exogenous entry), but allowing price level to adjust Change entry path and / or initial distribution Move back to steady-state entry levels Study time path back to steady state trade levels Compare trade with China and Japan if: All relationships are reset to new. One-time increase in exporters. Trade responses to the Great Recession

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Trade - CES aggregate

Figure: Experiment 1: Ending All Relationships

1.0 0.9 0.8 0.7 0.6 0.5

Japan China

0.4 0.3 5

0

5

Time

10

15

Total loss: 1.5 × annual steady state level of U.S. imports over 10 years. Monarch / Schmidt-Eisenlohr (FRB)

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Trade - CES aggregate

Figure: Experiment 2: One Period of Higher Entry

1.04 1.03 1.02 1.01

Japan China

1.00 5

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0

5

Time Learning in International Trade

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15

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Trade - CES aggregate

Figure: Experiment 3: Entry During the Great Recession

1.00 0.99 0.98 0.97

Japan China

0.96 5

Monarch / Schmidt-Eisenlohr (FRB)

0

5

Time Learning in International Trade

10

15

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In this paper, we have: Analyzed U.S. import data, focusing on importer-exporter relationship lengths and role of relationships. Proposed a model of learning consistent with observed patterns. Calibrated the model using U.S. import relationships with 20 partners. Demonstrated that the effects on trade from broken relationships and entry are long-lived.

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Thank You!

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[noframenumbering] Figure: Predicted Delivery Probabilities

1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0

A: Full model

2 4 6 8 10 C: No enforcement (λ =0)

2

4

Monarch / Schmidt-Eisenlohr (FRB)

6

8

10

B: No death shock (δ =0) 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0 2 4 6 8 10 1.1 D: Only patient firms (theta_hat=1) 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0 2 4 6 8 10

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[noframenumbering] Figure: Predicted Age Shares

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

A: Full model

2 4 6 8 10 C: No enforcement (λ =0)

2

4

Monarch / Schmidt-Eisenlohr (FRB)

6

8

10

B: No death shock (δ =0) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 2 4 6 8 10 D: Only patient firms (theta_hat=1) 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 2 4 6 8 10

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[noframenumbering] Figure: Predicted Trade Shares

0.35 0.30 0.25 0.20 0.15 0.10 0.05 0 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0

A: Full model

2 4 6 8 10 C: No enforcement (λ =0)

2

4

Monarch / Schmidt-Eisenlohr (FRB)

6

8

10

B: No death shock (δ =0) 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0 2 4 6 8 10 D: Only patient firms (theta_hat=1) 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0 2 4 6 8 10

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Basic Setup: Technology [noframenumbering] Consider a relationship between one importer and one exporter The exporter: Produces intermediate inputs q1 Decides on whether to exert effort in production: I I

gives rise to production costs c1 Iq ∈ {0, 1} (indicator for quality high or low)

The importer: Hires other inputs q2 at cost c2 in advance Assembles intermediate inputs into final good Production technology: q O = min{Iq × q1 , q2 }, ⇒ zero output if inputs are of low quality. ⇒ Given the Leontief technology and the pre-determination of q2 , firms optimally set q1 = q2 . Monarch / Schmidt-Eisenlohr (FRB)

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Basic Setup: Timing [noframenumbering] θb of suppliers are patient, while the rest are myopic. Timing I Importer and exporter agree on a trade: price, quantity + payment t=0 I I

t=1

I I I

I

structure Importer pays the exporter fraction α in advance Exporter receives money and decides whether to exert effort ⇒ patient supplier always exerts effort ⇒ myopic supplier only exert efforts when forced (probability λ) Importer receives goods and realizes profits (if good quality) Importer pays remaining amount (1 − α) if received good quality input: update beliefs (Bayes’ Rule) and trade again next period if received bad quality input: never trade again (trigger strategy)

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Basic Setup: Bayesian updating and delivery probability [noframenumbering] The posterior probability that a supplier is patient after buying from them for k periods is: θk =

θb 

 θb + 1 − θb λk

(10)

Call θek = θk + (1 − θk ) λ the delivery probability. I I

θk is the probability that the supplier is patient. (1 − θk ) λ is the probability that the supplier is not patient but the importer receives the inputs anyways.

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Static problem I [noframenumbering] For simplicity, assume zero financial interest rate. Then, expected profits from a supplier used for k periods: E [πk ] = θek (Rk − (1 − α)Tk ) − αTk − c2 qk

(11)

s.t.: αTk + (1 − α)Tk ≥ c1 qk (participation constraint patient exporter)

PC binding ⇒ Tk = T = c1 q1,k

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Static problem II [noframenumbering] Expected profits from a supplier used for k periods: E [πk ] = θek (Rk − (1 − α)c1 qk ) − (αc1 + c2 ) qk

(12)

FOC implies: R 0 (q) = (1 − α)c1 +

Monarch / Schmidt-Eisenlohr (FRB)

αc1 + c2 θek

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(13)

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CES Case I

[noframenumbering] Assume now that we have the following CES aggregator: Z

σ−1 σ



σ σ−1

dω

(14)

qt,k = pk−σ P σ Q,

(15)

Q=

q(ω) Ω

This delivers the standard demand:

with P =

R

Ω p(ω)

1−σ

Monarch / Schmidt-Eisenlohr (FRB)




1 1−σ

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CES Case II

[noframenumbering] The optimal price is then:   αc1 + c2 σ (1 − α)c1 + pk = σ−1 θek

(16)

Revenues (in case of successful production) are:  Rk =

σ σ−1

Monarch / Schmidt-Eisenlohr (FRB)

1−σ  (1 − α)c1 +

 αc1 + c2 PσQ e θk

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(17)

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[noframenumbering] Figure: Experiment 3: Permanent Increase in Entry

Two Country Example

Trade - CES aggregate

1.05 1.04 1.03 1.02 1.01

Germany Spain

1.00 5

0

5

Time

10

15

20

Parameters: λ=[ 0.33 0.37], θˆ =[ 0.21 0.08], δ =[ 0.23 0.24] Monarch / Schmidt-Eisenlohr (FRB)

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[noframenumbering] Figure: Experiment 3: Permanent Increase in Entry

All countries

Trade - CES aggregate

1.05 1.04 1.03 1.02 1.01 1.00 5

Monarch / Schmidt-Eisenlohr (FRB)

0

5

Time

10

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Good institutions tend to be complementary to long relationships.

1

Figure: Average Age of U.S. Import Relationships, 2011

TH JP BE

Country Fixed Effect 0 .5

IT

VE

CH CA DE

NP FI IL PH LK BY BB FR GB KN GRSI BO SE IE AT DO HN MX HU ZA LB SGNL IN HK PT PK PE DK BZ ES MYPL CZ UY AR KR UA BR SK NZ HT MG BS NO BG CL RU EG JM CR AU IS HR ID CO JO TN PA RO TR LU SV EE LS LT LV ECNG MA BD QA KE RS TT MT GT NI KW SA CN VN KH

ET BH

-.5

AF

-2

Monarch / Schmidt-Eisenlohr (FRB)

-1

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1

2

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